Phase diagram thermodynamic properties

The sequence of their occurrence is determined by the rates of chemical transformations at the interfaces. It cannot yet be theoretically predicted with full confidence for any particular reaction couple A-B. Having sufficient information on the equilibrium phase diagram, thermodynamics of chemical reactions, and the structure and physical-chemical properties of the compounds, it is possible to indicate those of them, which are most likely to occur and grow first at the A-B interface. 

These considerations indicate that structural (X-ray analysis, and optical and electron microscopy), relaxation (mechanical and dielectric relaxation, NMR, and RTL), and thermodynamic (phase diagrams, thermodynamic cycles, RGC) methods of investigation are currently used to determine the limits of the mutual solubihfy of polymers. At the same time it must be noted that evaluation of polymer compatibility is complicated by kinetic factors and because thermodynamically unstable systems are formed in the course of mixing of polymer. The effects of the nature of the polymers and of foreign impurities on compatibility do not yield to a complete explanation and this problem is far from being solved, despite its importance in the fact that the problem of modifying the properties of polymeric material is related to evaluation of the compatibility of polymers. 

IV. Phase Diagram, Thermodynamic, Dynamic and Structural Properties References... 

IV. PHASE DIAGRAM, THERMODYNAMIC, DYNAMIC AND STRUCTURAL PROPERTIES... 

E. A. Brandes and R. E. Flint, Manganese Phase Diagrams, The Manganese Centre, Paris, 1980 L. B. Pankratz, Thermodynamic Properties of Elements and Oxides, Bull. 672, U.S. Bureau of Mines, Washington, D.C., 1982. 

Nevertheless, large-scale phenomena and complicated phase diagrams cannot be investigated within realistic models at the moment, and this is not very likely to change soon. Therefore, theorists have often resorted to coarse-grained models, which capture the features of the substances believed to be essential for the properties of interest. Such models can provide qualitative and semiquantitative insight into the physics of these materials, and hopefully establish general relationships between microscopic and thermodynamic quantities. 

M. J. Vlot, S. Claassen, H. E. Huitema, J. P. v. d. Eerden. Monte Carlo simulation of racemic liquid mixtures thermodynamic properties and local structures. Mol Phys 97 19, 1997 M. J. Vlot, J. C. v. Miltenburg, H. A. Oonk, J. P. V. d. Eerden. Phase diagrams of scalemic mixtures. J Chem Phys 707 10102, 1997. 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

Fig. 2.37. Phase diagram for Ca0-Na20 Si02-(Al203)-H20 system in equilibrium with quartz at 400°C and 400 bars. Plagioclase solid solution can be represented by the albite and anorthite fields, whereas epidote is represented by clinozoisite. Note that the clinozoisite field is adjacent to the anorthite field, suggesting that fluids with high Ca/(H+) might equilibrate with excess anorthite by replacing it with epidote. The location of the albite-anorthite-epidote equilibrium point is a function of epidote and plagioclase composition and depends on the model used for calculation of the thermodynamic properties of aqueous cations (Berndt et al., 1989).

The thermodynamic properties of a number of compounds are shown in Appendix D as pressure-enthalpy diagrams with lines of constant temperature, entropy, and specific volume. The vapor, liquid, and two-phase regions are clearly evident on these plots. The conditions under which each compound may exhibit ideal gas properties are identified by the region on the plot where the enthalpy is independent of pressure at a given temperature (i.e., the lower the pressure and the higher the temperature relative to the critical conditions, the more nearly the properties can be described by the ideal gas law). 

A convenient starting point is to consult the phase diagrams in Hansen s Constitution of Binary Alloys (10) and supplementary volumes (11,12), but information may also be needed on miscibility at the temperatures normally employed for film preparation and catalytic reaction. Therefore, some consideration must be given to the thermodynamic properties of the... 

Now we consider thermodynamic properties of the system described by the Hamiltonian (2.4.5) it is a generalized Hamiltonian of the isotropic Ashkin-Teller model100,101 expressed in terms of interactions between pairs of spins lattice site nm of a square lattice. Hamiltonian (2.4.5) differs from the known one in that it includes not only the contribution from the four-spin interaction (the term with the coefficient J3), but also the anisotropic contribution (the term with the coefficient J2) which accounts for cross interactions of spins a m and s m between neighboring lattice sites. This term is so structured that it vanishes if there are no fluctuation interactions between cr- and s-subsystems. As a result, with sufficiently small coefficients J2, we arrive at a typical phase diagram of the isotropic Ashkin-Teller model,101 102 limited by the plausible values of coefficients in Eq. (2.4.6). At J, > J3, the phase transition line... 

This chapter introduces additional central concepts of thermodynamics and gives an overview of the formal methods that are used to describe single-component systems. The thermodynamic relationships between different phases of a single-component system are described and the basics of phase transitions and phase diagrams are discussed. Formal mathematical descriptions of the properties of ideal and real gases are given in the second part of the chapter, while the last part is devoted to the thermodynamic description of condensed phases. 

Calculation, thermodynamic optimization of phase diagrams. The knowledge of phase equilibria, phase stability, phase transformations is an important reference point in the description and understanding of the fundamental properties of the alloys and of their possible technological applications. This interest has promoted a multi-disciplinary and multi-national effort dedicated not only to experimental methods, but also to techniques of optimization, calculation and prediction of... 

It has already been noticed (see 3.9.4) that according to the mentioned concepts several ternary compounds may be considered as the result of a sort of structural interaction between binary compounds. As a consequence some regular trend could also be predicted for their occurrence in their phase diagrams and in the description (and perhaps modelling) of their thermodynamic properties. A few details about this type of structural relationships will be considered in the following and, in this introduction, examples of blocks of simple structural types and of their combination in more complex types will be described. 

Figure 13.5. The phase diagram for the system Ag-Cu at constant pressure. With permission, from R. Hultgren, R D. Desai, D. T. Hawkins, M. Gleiser, and K. K. Kelley, Selected Values of Thermodynamic Properties of Binary Alloys, American Society of Metals, Metals Park, OH, 1973, p. 46.

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